References
- Lieb EH. Existence and uniquenness of the minimizing solution of Choquard nonlinear equation. Stud. Appl. Math. 1977;57:93–105.
- Lieb EH, Simon B. The Hartree--Fock theory for Coulomb systems. Commun. Math. Phys. 1977;53:185–194.
- Penrose R. On gravity’s role in quantum state reduction. Gen. Relativ. Gravitation. 1996;28:581–600.
- Lions PL. The Choquard equation and related questions. Nonlinear Anal. TMA. 1980;4:1063–1073.
- Ackermann N. On a periodic Schrödinger equation with nonlocal superlinear part. Math. Z. 2004;248:423–443.
- Cingolani S, Clapp M, Secchi S. Multiple solutions to a magnetic nonlinear Choquard equation. Z. Angew Math. Phys. 2012;63:233–248.
- Cingolani S, Secchi S, Squassina M. Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities. Proc. R. Soc. Edinburgh Sect. A. 2010;140:973–1009.
- Lions PL. The concentration-compactness principle in the calculus of variations. The locally compact case. II. Ann. Inst. H. Poincaré Anal. Non Linéaire. 1984;1:223–282.
- Menzala GP. On regular solutions of a nonlinear equation of Choquard type. Proc. R. Soc. Edinburgh. Sect. A. 1980;86:291–301.
- Nolasco M. Breathing modes for the Schrödinger--Poission system with a multiple-well external potential. Commun. Pure Appl. Anal. 2010;9:1411–1419.
- Lozano S, Cecilia D. Elliptic problem with local and nonlocal nonlinearities in exterior domains. Available from: http://www.posgrado.unam.mx/publicaciones/ant_col-posg/.
- Tod P, Moroz MI. An analytical approach to the Schrödinger--Newton equations. Nonlinearity. 1999;12:201–216.
- Wei J, Winter M. Strongly interacting bumps for the Schrödinger--Newton equations. J. Math. Phys. 2009;50:22pp.
- Ma L, Zhao L. Classification of positive solitary solutions of the nonlinear Choquard equation. Arch. Ration. Mech. Anal. 2010;195:455–467.
- Chen WX, Li CM, Ou B. Classification of solutions for an integral equation. Commun. Pure Appl. Math. 2006;59:330–343.
- Moroz V, Van Schaftingen J. Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay estimates. J. Funct. Anal. 2014;265:153–184.
- Moroz V, Van Schaftingen J. Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains. J. Differ. Equ. 2013;254:3089–3145.
- Choquard P, Stubbe J, Vuffracy M. Stationary solutions of the Schrödinger--Newton model-an ODE approach. Differ. Interal Equ. 2008;27:665–679.
- Lieb EH, Loss M. Analysis. 2nd ed. Vol. 14, Graduate studies in mathematics. Providence, RI: AMS; 2001.
- Willem M. Minmax theorems. Vol. 24, Progress in nonlinear differential equations and their applications. Boston: Birkhäuser; 1996.